The mass of grapes sold per day by a large shop can be modelled by a normal distribution with mean 28 kg. On 10% of days less than 16kg of grapes are sold.

Mark scheme

Marking points from the official mark scheme (May/June 2023). The mark or mark type is shown in brackets.

1. [B1] ±1.282 seen, cao critical value.
2. [M1] Use of the standardisation formula with 16, 28, σ and a z-value (not 0.1, 0.9, 0.282, 0.5398, 0.8159) equated to a z-value.
3. [M1] Condone continuity correct ±0.5, not σ², √σ.
4. [M1] Condone (16-28)/σ = -1.282 .
5. [A1] σ = 9.36
6. [M1] One term ¹²Cx (p)ˣ (1-p)¹²⁻ˣ, 0 < p < 1. x ≠ 0,1,2.
7. [A1] Correct expression, accept unsimplified, no terms omitted leading to final answer.
8. [B1] 0.1108699... rounded to at least 3SF.
9. [B1] Identifying at least one of -1.3 or 1.3 as the appropriate z-values.
10. [M1] Calculating the appropriate probability area from 2 symmetrical z-values (leading to their final answer, expect > 0.5).
11. [A1] 0.8064, 0.806 < p < 0.8065 .
12. [B1 FT] Strict FT their at least 4-figure probability (not z-value). Final answer must be positive integer, no approximation or rounding stated.